In triangle abc, the measure of angle bca is 90, segment ac is 12 units, and segment bc is 9 units. if d is a point on hypotenuse ab, such that segment ad is 5 units, what is the length of segment cd? express your answer is simplest radical form.

CD = 6 units

Step-by-step explanation:

In triangle ABC , AB is the hypotenuse then    AB =√(BC)² + (AC)²  = √(12)² + (9)²   =  15

AB = 15

sin ∠ABC  12/15   = 0,8   Then   arcsin (0.8)  =  53,1°

∠ABC  = 53,1°      and   ∠BAC  =  36,9°

Now the hypotenuse is 15 units and we need to find the lenght of segment

CD. If we divide the hypotenuse in three equal segment (of lenght 5 each) we at the same time are dividing the ∠ACB ( 90°),  in three equals angles of

30°.

If we now apply sin law

sin 30°/ 5    = sin 36,9°/CD

Then    CD  = 5 * sin 36.9° / sin 30°   ⇒  CD =[ 5* (9/15) ] / 1/2

CD = 6 units

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form